The aim of this paper is to discuss the value distribution of the function f(k) - afn. Under the assumption that f(z) is a transcendental meromorphic function in the complex plane and a is a non-zero constant, it is proved that if n ≥ k + 3, then f(k) - afn has infinitely many zeros. The main result is obtained by using the Nevanlinna theory and the Clunie lemma of complex functions.
ZHANG Zhanliang
. On value distribution of f(k) - afn[J]. Frontiers of Mathematics in China, 2006
, 1(4)
: 612
-619
.
DOI: 10.1007/s11464-006-0032-8